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Porosity and Mechanical Properties of Mesoporous Thin Films Assessed by Environmental Ellipsometric Porosimetry Ce´dric Boissiere,† David Grosso,† Sophie Lepoutre,† Lionel Nicole,† Aline Brunet Bruneau,‡ and Cle´ment Sanchez*,† Laboratoire de Chimie de la Matie` re Condense´ e, Universite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, Cedex 5, France, and Institut des Nanosciences de Paris, UMR CNRS 7601, Universite Paris 6, Campus Boussicaut, 140 Rue Lourmel, 75015 Paris, France Received April 13, 2005. In Final Form: July 22, 2005 Mesoordered silica thin films with cubic structures were prepared by evaporation induced self-assembly (EISA) with two types of structuring agent (CTAB and block copolymer F127). A complete and accurate description of these films was obtained by combining 2D-SAXS analyses, variable angle spectroscopic ellipsometry, and a specially designed environmental ellipsometric porosimetry (EEP) experiment. The EEP analysis is rapid and cheap and operates at ambient pressure and temperature. This latter experiment was performed with water and produced a set of water adsorption-desorption isotherms. A modified Kelvin equation, coupled with a modelisation of pores contraction, enabled the determination of the structural parameters of films porous networks: ellipsoidal pore diameters, porous volume, and surface area. Young moduli of films in the direction perpendicular to the substrates were calculated from these parameters.
Introduction Porous thin films (typically thinner than 2 microns) are having more and more importance in modern material science due to their numerous high added value applications in energy transfer devices, microelectronic low dielectric constant films, or selective sensors.1-4 For several years, a growing effort has been made to develop new simple, rapid, non destructive and reliable techniques allowing the characterization of the porous structure of films for industrial production controls and laboratory investigations. Ellipsometric Porosimetry (EP), first reported by Baklanov and co-workers in 2000,5,6 is a very powerful technique for micro- and mesopores characterization of supported porous thin films. This technique consists of plotting an adsorption-desorption isotherm from the variations of film refractive index induced by the change of partial pressure of an organic solvent above a film. The device is usually based on the coupling of a pressure controlled chamber (conventional in gas volumetry characterization devices) and a spectroscopic ellipsometer. Pore size distribution of micro- and mesopores of the film can then be directly obtained via porosimetry models usually based on the Kelvin equation for the determination of mesopores sizes5 or different models such as the Dubinin Raduchkevich (DR) model for the deter* To whom correspondence should be addressed. Phone: 00 33 1 44 27 55 42. E-mail:
[email protected]. † Universite ´ Pierre et Marie Curie, Jussieu. ‡ Universite ´ Pierre et Marie Curie, Boussicaut. (1) De Theije, F. K.; Balkenende, A. R.; Verheijen, M. A.; Baklanov, M. R.; Mogilnikov, K. P.; Furukawa, Y. J. Phys. Chem. B 2003, 107, 4280. (2) Innocenzi, P.; Martucci, A.; Guglielmi, M.; Bearzotti, A.; Traversa, E.; Pivin, J. C. J. Eur. Ceram. Soc. 2001, 21 (10-11), 1985. (3) Gimon-Kinsel, M. E.; Balkus, K. J., Jr. Microporous Mesoporous Mater. 1999, 28 (1), 113. (4) Nicole, L.; Boissie`re, C.; Grosso, D.; Hesemann, P.; Moreau, J.; Sanchez, C. Chem. Commun. 2004, 2312. (5) Baklanov, M. R.; Mogilnikov, K. P.; Polovinkin, V. G.; Dultsev, F. N. J. Vac. Sci. Technol. B 2000, 18 (3), 1385. (6) Baklanov, M. R.; Mogilnikov, K. P. Mater. Res. Soc. 2001, 616, D4.2.1.
mination of micropores sizes.7 In industry, EP devices are more and more used for quality control of high technology micro- and mesoporous inorganic or hybrid films (such as flat computer screens and low-k layers in microelectronic). Surprisingly, so far, the only EP device available is commercialized by SOPRA Co.8 In academic and applied research, EP was first used for the characterization of amorphous porous thin layers, and rapidly extended to the determination of the pore size distribution (PSD) of thin layers of mesostructured silica9 and of organically modified silica films produced by the evaporation induced self-assembly (EISA) process.1 For porous silica films, spectroscopic infrared ellipsometry gives very useful supplementary information on a film chemical composition.10 So far, the accuracy of the EP technique has been limited by two categories of problems. The first limitation comes from the assumption that an adsorbate in confined environments retains its bulk properties (polarizability, volume, and surface tension). The error introduced here depends a lot on both the adsorbate and the chemical surface to be analyzed.11,12 The higher the polarizabilities of adsorbate and surface, the larger the distortion induced by the porous confinement on the above-mentioned properties. The second limitation is that, so far, porosimetry models used with the EP technique are directly inherited from powder volumetry techniques and are not entirely adapted to films specificities. In these models, the geometry of pores is often assumed to be cylindrical or spherical. For mesostructured films, the unidirectional pore shrinkage associated to the drying and treatment (7) Dultsev, F. N. Thin Solid Films 2004, 458, 137. (8) SOPRA; Optical solutions: Bois-Colombes, France. www.soprasa.com. (9) Bourgeois, A.; Bruneau, A. B.; Fisson, S.; Demarets, B.; Grosso, D.; Cagnol, F.; Sanchez, C.; Rivory, J. Thin Solid Films 2004, 447, 46. (10) Brunet-Bruneau, A.; Besson, S.; Gacoin, T.; Boilot, J. P.; Rivory, J. Thin Solid Films 2004, 447, 51. (11) Gregg, S. J.; Sing, K. S. W. Adsorption, surface area and Porosity; Harcourt Brace and Co.: Orlando, FL, 1997. (12) Boissie`re, C.; Brubach, J. B.; Mermet, A.; de Marzi, G.; Bourgaux, C.; Prouzet, E.; Roy, P. J. Phys. Chem. B 2002, 106, 1032.
10.1021/la050981z CCC: $30.25 © 2005 American Chemical Society Published on Web 11/23/2005
Properties of Mesoporous Thin Films
lead to nonsymmetrical models. PSD assuming spherical geometry is thus not accurate. Moreover, the pore surface wettability is usually assumed to be perfect in Kelvin methods and is thus usually not taken into account.11 Since wettability is a crucial factor of the capillary condensation, we will show here that the liquid-solid contact angle, characterizing the surface energy, is needed to give a correct interpretation of the water adsorption-desorption isotherm. The goal of this work is to develop a simple, general and reliable analytic approach, allowing direct characterization of mesoporous layers (including EISA processed layers) that takes into account pore geometry, pore size, surface area, porous volume, and mechanical properties (usually the stiffness and/or the Young modulus). Thus, we concomitantly report the development of the first environmental ellipsometric porosimetry (EEP) device designed to allow fast film characterization at ambient pressure and temperature. To make mesopore size investigation simple, cheap, and non toxic, we performed EEP measurements using a pulsed air flow with controlled partial pressure of water. This system allows a fast partial pressure equilibration at each point of the isotherm (a complete adsorption-desorption cycle can be obtained within 40 min time), whereas the actual commercial EPs with sealed vacuum chamber have to work with a gradient of absolute pressure (preventing equilibration) to obtain fast measurements. To validate the porous network characterization with EEP, we used mesoporous films made by EISA with known mesoporous networks as test materials. Indeed one can control their structure at many different levels: (i) meso-ordered pore size can be tuned between 2 and 30 nm, (ii) periodical order of the porous network can be either 2D or 3D, (iii) the inorganic wall composition is tunable, and (iv) wall can be either amorphous or nanocrystalline. Thus, one can modulate their chemical and physical properties in a very wide range.13-20 Two silica films with cubical ordered mesostructures were used. To improve the EP method, a precise analysis of film contractions was performed via the combination of 2D small-angle X-ray scattering (2DSAXS), ellipsometry, transmission electronic microscopy (TEM), and EEP analyses. A model was introduced to take into account the uniaxial contraction of the inorganic network during thermal treatments which transforms the spherical shape of cubic mesostructured domains into ellipsoidal pores. Calculating the anisotropy of these pores and reintroducing the liquid-solid contact angle allowed us to produce a better modified Kelvin equation for pore size determination and to rationalize some capillary condensation domain shifts due to the evolutions of (13) Cagnol, F.; Grosso, D.; Soler-Illia, G. J. d. A. A.; Crepaldi, E. L.; Babonneau, F.; Amenitsch, H.; Sanchez, C. J. Mater. Chem. 2003, 13, 61-66. (14) Klotz, M.; Albouy, P.-A.; Ayral, A.; Me´nager, C.; Grosso, D.; van der Lee, A.; Cabuil, V.; Babonneau, F.; Guizard, C. Chem. Mater. 2000, 12, 1721. (15) Gibaud, A.; Grosso, D.; Smarsly, B.; Baptiste, A.; Bardeau, J. F.; Babonneau, F.; Doshi, D. A.; Chen, Z.; Brinker, C. J.; Sanchez, C. J. Phys. Chem. B 2003, 107 (25), 6114. (16) Lu, Y.; Ganguli, R.; Drewien, C. A.; Anderson, M. T.; Brinker, C. J.; Gong, W.; Guo, Y.; Soyez, H.; Dunn, B.; Huang, M. H.; Zink, J. I. Nature 1997, 389 (6649), 364. (17) Besson, S.; Gacoin, T.; Jacquiod, C.; Ricolleau, C.; Babonneaud, D.; Boilot, J.-P. J. Phys. Chem. B 2000, 104, 12095. (18) Crepaldi, E. L.; Soler-Illia, G. J. d. A. A.; Grosso, D.; Cagnol, F.; Ribot, F.; Sanchez, C. J. Am. Chem. Soc. 2003, 125, 9770. (19) Grosso, D.; Cagnol, F.; Soler-Illia, G. J. d. A. A.; Crepaldi, E. L.; Amenitsch, H.; Brunet-Bruneau, A.; Bourgeois, A.; Sanchez, C. Adv. Funct. Mater. 2004, 14 (4), 309. (20) Grosso, D.; Boissiere, C.; Smarsly, B.; Brezesinski, T.; Pinna, N.; Albouy, P. A.; Amenitsch, H.; Antonietti, M.; Sanchez, C. Nat. Mater. 2004, 3, 787.
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Figure 1. Scheme of experimental ellipsoporometer.
adsorbate/surface interactions. Finally, we studied and discussed here the influence of pore anisotropy on Young modulus determination. Experimental Section Silica films with cubic Pm3n and Im3m ordered mesostructures were prepared, as reported previously, in the presence of cethyltrimethylammonium bromide (CTAB) or F127 Pluronic block copolymer as structuring agents.19,21 Solutions were prepared for dip-coating with a molar composition of 1 TEOS: 40 EtOH: 5 H2O: 0.15 HCl: 0.14 CTAB (or 4 × 10-3 F127 respectively) and aged at 80 °C for 20 min. All products were purchased from Sigma/Aldrich and used as furnished. Thin films were prepared by dip coating silicon wafers of thickness 8 µm (for 2D-SAXS measurements) and one side polished 350 µm thick for EEP experiments. Films were dip coated at a withdrawal speed of 2.7 mm s-1 and left for rest 10 min in a 50% relative humidity (RH) atmosphere. This experimental protocol was followed to obtain films with cubic mesostructures, optical homogeneity, and transparency. They were then kept in sealed flasks at 100 °C at least 1 day before calcination in air at 500 °C for 10 min (5°/min gradient). The removing of organic parts by calcination led to ordered mesoporous silica films with monodisperse pores having different sizes. 2D-SAXS measurements were performed with third generation synchrotron radiations (SAXS beam line of ELETTRA, Trieste, Italy). Ellipsometry measurements were performed on a UV-visible (from 240 to 1000 nm) Variable Angle Spectroscopic Ellipsometer (VASE) from Woolam, and the data analysis was performed with the WVase32 software. The two types of periodically organized mesoporous networks prepared were named accordingly with the structuring agent name and the calcination temperature T. Hence, silica films produced from CTAB and silica are labeled CS-T, and those produced with block copolymer F127 and silica are labeled FS-T. Transmission electronic microscopy (TEM) pictures were obtained with a JEOL CX/STEM. EEP produced adsorption-desorption isotherms were analyzed via the IIC pore contraction model and a modified Kelvin equation (vide infra). The EEP setup used is represented in Figure 1. It is made of the previously described ellipsometer on which is fixed a cell of environment control containing the film to analyze. In laboratories, gas volumetry analyses are usually time-consuming, mainly because of long pressure equilibration time within the analysis chamber. In the experimental setup of these experiments, we replaced the pressure equilibration system by a continuous flux of air containing a fixed partial pressure of adsorbate directly in contact with the mesoporous film to analyze. This procedure eliminates the dead volume effect of the analysis chamber always encountered with pressurized techniques. In addition, the flux in itself helps the rapid equilibration at low (21) Falcaro, P.; Grosso, D.; Amenitsch, H.; Innocenzi, P. J. Phys. Chem. B 2004, 108 (30), 10942.
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relative pressure by enhanced gas convection.22 Though, working at atmospheric pressure limits the choice of efficient adsorbates for EEP measurements. Indeed, with atmosphere molecules being a huge majority in the gas flux, we had to select a chemical compound at the same time volatile at ambient temperature and presenting an affinity with silica strong enough to neglect the adsorption competitions at the surface of mesopores. Here we used water as the adsorbate considering its well documented affinity for silica surfaces.10,11,23-25 For measurement, the cell temperature was fixed at 23 °C and was continuously filled by 2.5 L/min flux of air with a controlled water partial pressure. Experimental Protocol of EEP Analysis. Typically, the ordered porous structure characterization method described in this article was performed in 4 steps, aiming at the determination of pores anisotropy, the plotting of a water adsorption-desorption isotherm of the mesoporous film, and the calculation of its porous parameters (porous volume, pore anisotropy, and size and surface area). The uniaxial young modulus (direction orthogonal to the substrate) was extracted from these results, as described in the discussion. Step I: Determination of Pores Anisotropy. It consists of the preparation at ambient temperature of two films, the organic/ inorganic mesostructured film, and a reference film prepared in the same conditions but containing no structuring agent. The reference film optical properties were assumed identical to those of silica walls of the mesostructured films. Optical constants of both films were determined by ellipsometry (in dry atmosphere), and the mesostructure organization was characterized by 2DSAXS. An identical thermal treatment was then applied on both films, as detailed here after. The reference film was used to simulate the contraction behavior of the silica walls of the mesoporous network. Upon heating, spherical pores of the hybrid film flatten and become ellipsoidal. Final contractions of reference and mesostructure films were then determined by ellipsometry and used for the calculation of pores anisotropy via the isotropic inorganic contraction model which separates contraction contributions of the silica matrix and the mesostructure (vide infra the theoretical section). Step II: Film Porous Volume and EEP Isotherm Determinations. The optical method used for the porous volume and isotherm determinations is usually based on the Lorentz-Lorentz equation which uses the optical index of the film analyzed and requires the macroscopic polarizability and molar volume of the adsorbed molecule.5 In this work, the use of water as adsorbate in mesopores made the usual macroscopic description of water unreliable. Indeed, many works on water confining showed that highly curved water interfaces or confined water droplets have density, surface tension, and hydrogen bond network differing significantly from that of the bulk.11,12,26,27 To overcome this problem, we calculated the volume of water adsorbed into the porous network with the Bruggemann effective medium approximation (BEMA) model, sometimes referred to as coherent potential approximation (eq 1). It allowed the determination of the relative volumetric fractions fA and fB of two materials A and B of known dielectric constants ˜ A and ˜ B within a volume unit of measured dielectric constant ˜ . This equation takes into account the complex expression of the refractive index and is very accurate for a two component system
Figure 2. The A film porous volume Vp is determined by fitting with BEMA the volumetric fraction of void and reference film of the dry stabilized mesoporous film. Vwater/Vfilm adsorbed is determined by fitting with BEMA the volumetric fraction of the dry stabilized mesoporous film A and the water saturated mesoporous film B. The porous volume Vp of the mesoporous layer (measured in dry atmosphere) was determined with the BEMA by fitting the volumetric fractions of air and the silica matrix (which optical properties were obtained from the measurement of the reference film in step I) within the mesoporous film (Figure 2). The evolution of film refractive index n and thickness d as a function of the relative humidity (RH), n ) F(RH), and d ) F(RH), were measured by EEP. The adsorption-desorption isotherm VWATER/VFILM ) F(RH) was then determined with the BEMA by fitting the n ) F(RH) curve at each RH in order to determine volumetric fractions fB of the water-saturated mesoporous film B and fA of the dry mesoporous film. VWATER/VFILM was then assumed to be equal to the product of the porous volume and the volumetric fractions of the water-saturated mesoporous film (eq 2)
VWATER/VFILM ) fBVp
(2)
Step III: EP Determination of Water Layer Thickness Adsorbed at Each RH. This step allowed the determination of the thickness of water t adsorbed onto a flat surface of a reference SiO2 film, assumed to give equivalent adsorption behavior than mesopores surface. t is directly measured by ellipsometry at each RH to produced the t ) F(RH) isotherm which is needed for the pore size determination in Step IV. Step IV: Isotherm Analysis, Porous Network, and Mechanical Characterization. The pore size distribution (PSD) was determined from the isotherm obtained in Step II via a modified Kelvin equation taking into account the pore anisotropy (Step I) and the water layer thickness t (Step III). The film surface area was obtained via a t-plot treatment of the isotherm. Finally, the orthogonal Young modulus of the mesoporous film was extracted from the d ) F(RH) experimental curve via a combination of the Young-Laplace and the modified Kelvin equations (3) and (4) of the theoretical section.
Theoretical Section ˜ A - ˜ ˜ B - ˜ + fB )0 fA ˜ A + 2˜ ˜ B + 2˜
(1)
(22) This effect is assumed not disturbing the capillary condensation phenomenon attending that the air flow on top of the film is laminar (circulation speed within the analysis chamber is 8 cm/s) and that the very small pressure of the air flux onto the film surface is negligible if compared with capillary pressure difference taking place within the film during the water condensation. (23) Llewellyn, P. L.; Schu¨th, F.; Grillet, Y.; Rouquerol, F.; Rouquerol, J.; Unger, K. K. Langmuir 1995, 11, 574. (24) Cauvel, A.; BruneI, D.; Di Renzo, F. Langmuir 1997, 13, 2773. (25) Yanagisawa, N.; Fujimoto, K.; Nakashima, S.; Kurata, Y.; Sanada, N. Geochim. Cosmochim. Acta 1997, 61 (6), 1165. (26) Smirnov, P.; Yamaguchi, T.; Kittaka, S.; Takahara, S.; Kuroda, Y. J. Phys. Chem. 2000, 104, 5498. (27) Tolman, R. C. J. Chem. Phys. 1949, 17 (3), 333.
Volumetric Pore Size Determination. The pore size determination was based on the Kelvin equation (3) which gives the relation between the relative pressure P/P0 of an adsorbate, the liquid-air surface tension γ of a curved interface,28 and the adsorbate liquid-interface surface area variation dS, when the volume V of adsorbate evolves of dV.11,29 θ is the solid/liquid wetting angle, and VL is the molar volume of the adsorbate after capillary condensation. Considering that metal oxide surfaces adsorbs very preferentially water to air molecules (N2, O2, and CO2), (28) Modified accordingly to the Tolman model to take into account the decrease of surface tension due to the high curvature of liquid interfaces in mesoporous networks. (29) Galarneau, A.; Desplantier-Giscard, D.; Dutarte, R.; Di Renzo, F. Microporous Mesoporous Mater. 1999, 27, 297.
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Figure 3. Kelvin equation modified for spherical ellipsoid pores, taking into account Tolman correction of the water surface tension for highly curved domains and the pore anisotropy p given by the IIC contraction model. The resulting geometric factor as a function of pore anisotropy is represented.
we assumed that the RH is equal to the partial pressure P/P0 of the Kelvin equation
RT ln
P dS ) γVL cos θ P0 dV
(3)
The Kelvin equation (4) was calculated for sphericellipsoidal pores of anisotropy p (where p ) a/b, is the ratio of the ellipse large radius a on small radius b)
RT ln
[
]
C P ) - γVL cos θ 1 + 2 /b P0 2p
(4)
with
ln C)
[11 -+ EE] E
Figure 4. IIC lattice contraction model description. Black arrows represent the contraction directions of inorganic walls.
Isotropic Inorganic Pore Contraction (IIC) Model. The IIC model is based on the hypothesis that the contraction of mesostructured films can be described by an ellipsoidal contraction of pores resulting from the contraction of the mesostructure lattice, plus a simultaneous isotropic contraction of silica walls between mesodomains (Figure 4). The isotropic walls contraction is assumed to be equal to the uniaxial contraction of the reference film at the power 1/3. The IIC model is supported by the fact that, contrary to pure silica reference films in which silica contraction can only be macroscopically relaxed in the direction normal to the substrate, in mesostructured films, the in-plane contraction may be locally relaxed by the deformation of the mesopores. The anisotropy parameter p can then be obtained in a very simple way by the eq 5 in which dFILM T and dREF T are thicknesses of mesostructured and reference films obtained by ellipsometry at the temperature T. The same anisotropy parameter can be obtained if dFILM T values are the d spacing values obtained from XRD experiments in Bragg Brentano geometry
p)
and 2
E)
(p - 1) p
1/2
the eccentricity factor. A similar calculation for a cylindrical interface is reported in Appendix I with the demonstration of eq 4. The representation of the geometric coefficient G ) [1 + C/2p2] (Figure 3) as a function of the anisotropy p highlights that the Kelvin radius determination is very sensitive to the value of p, especially when it ranges between 1 and 3. A p value of 1 (case of a spherical interface) gives back the well-known Kelvin geometric factor G of 2. Interestingly, if the p value increases up to 3, G decreases down to 1.21, changing dramatically the calculated value of the pores small diameter b. Obviously, one meets here a problem of pore size determination as the Kelvin relation (4) contains two unknown parameters, b and p. To solve this problem, we determined the pore anisotropy with a pore contraction model named isotropic inorganic contraction (IIC; Figure 4). When p is known, the pore small radius can be calculated by adding the Kelvin radius b to the thickness t of the water layer adsorbed at the RH of the capillary condensation: b(pore) ) b(Kelvin) + t.11 Hereafter, we propose a simple model describing the contraction of amorphous metaloxide-based films, aimed at the prediction of the final anisotropy of the mesopores and based on film thickness values before and after calcination.
(
)
dFILM 25 dREF.T dFILM‚T dREF 25
1/3
(5)
Finally, the IIC model does not imply that the reference film contraction has to be inferior or equal to the mesostructured film contraction. Hence, it can be used to describe mesodomains flattening whatever the calcination temperature, before or after the removal of structuring agents. Results and Discussion Two types of mesoporous films with cubic ordered mesodomains were prepared by the EISA method following previously reported protocols. They were analyzed by ellipsometry and 2D-SAXS and heated at 100 °C for one night before any further treatment. TEM pictures of these mesostructures are given in Figure 5. 2D-SAXS experiments (not shown here) confirmed the cubic space group of CS-25 with a Pm3n symmetry and of FS-25 with a Im3m symmetry.13,21 Diffraction spots assignment evidenced that, in the as-made films, both mesostructures are noncontracted. Study of Films Contraction during Calcination. As reported in the literature, structuring agents are commonly removed by calcination at a temperature equal to or higher than 500 °C. Upon calcination in air from 100 to 500 °C (5°/min gradient), ellipsometry and 2D-SAXS analyses showed that films constantly shrink in the direction perpendicular to the substrate. For mesostructured frameworks, the isotropic lattice contraction, well
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(/nm) 25 °C 500 °C contraction rate
Figure 5. TEM pictures of silica films prepared with CTAB and F127 structuring agents after heat treated at 100 °C. Insert: simplified Pm3n structure of as made CTAB films and Im3m structure of as made F127 films.
Figure 6. Pure SiO2, CS and FS film contractions with temperature obtained from ellipsometry measurements. (×) FS-500 and (+) CS-500 contractions obtained by LAXRD and SAXS analyses (from refs 20 and 27).
documented for the calcination of analogous powders, was for a large part due to the water loss and to the condensation of the silica network.30 The evolution of films thicknesses as a function of calcination temperature, reported in Figure 6, showed that the reference SiO2 film contracted more than hybrid ones at low temperature (T < 150 °C), but less above 200 °C. This behavior is due to the presence of the amphiphilic molecules in hybrid films which volume is fixed (neglecting thermal dilatation) from ambient temperature up to the decomposition temperature (starting at 150 and 250 °C respectively for F127 copolymer and CTAB). At low temperature, the hybrid films contraction is thus limited to the volumetric contraction of their silica fraction. At temperatures higher than 200 °C, the thickness decrease is cumulatively due to the contraction of silica walls and porous uniaxial structure contraction in the direction orthogonal to the substrate. The final contractions at 500 °C, reported in Table 1, are 21.9%, (30) Innocenzi, P.; Falcaro, P.; Grosso, D.; Babonneau, F. J. Phys. Chem. B 2003, 107 (20), 4711.
CS thickness
FS thickness
simple SiO2 film thickness
CS GISAXS
FS GISAXS
239.8 170.3 29.0%
186.7 111.3 40.4%
63.9 49.9 21.9%
≈30%
≈42%
29%, and 40.4% respectively for reference films SiO2, CS500, and FS-500. Monitored by 2D-SAXS, this macroscopic contraction was shown to be concomitant with a progressive contraction of the mesostructures in the direction orthogonal to the substrate. Deformation of original cubic lattices of CS and FS films were observed along the [211] and [110] directions respectively, and no in-plane contraction (parallel to the substrate) was observed. Finally, with films macroscopic contractions and mesostructures contractions values (Table 1) being very close, we concluded that mesostructure lattice contractions of silica mesoporous films can be quantified with a good accuracy by a simple ellipsometric monitoring of films thicknesses. We assumed in this article that this uniaxial contraction induced a transformation of the pores from spherical to ellipsoidal shape. The IIC model, detailed in the theoretical section, describes the film contraction as the result of the uniaxial pores flattening and the silica wall isotropic contraction. Hence, the thicker the silica wall in one direction, the wider the pore dimension increases in this direction. For FS-500 films, the Fmmm final symmetry group of the contracted mesostructure implies that the ellipsoidal shape of pores tends to become a truncated and contracted octahedron.21 On the other hand, in CS-500 films, the contraction of the Pm3n symmetry along the [211] direction leads to two different pore environments. A quarter of the pores present a “flattened” icosahedral deformation, and a complex nonisotropic transformation occurs for the others. Therefore, describing the pore geometry with high precision is only possible with computational modelisation. In this work, we assumed that the final dS/dV expression of the Kelvin equation of the real pores shape does not differ significantly from the ellipsoidal geometry. The anisotropy factor calculated for the SF-500 film was equal to 1.55 (leading to a G value of 1.55), whereas the anisotropy factor calculated for the CS-500 film was 1.33 (leading to a G value of 1.71). Hence, a significant pore deformation was observed after calcination at 500 °C for both mesostructures. In these cases, the anisotropy correction of the Kelvin equation allowed corrections of the pore size values as high as 24.7% if compared with a simple spherical pores model. Therefore, pore size contraction is in no way a negligible parameter and will be of paramount importance, especially for pore size determination of non-silica films whose contractions are much higher than contractions of the present silica films. Another example of the tremendous influence of pores anisotropy was recently published. This publication describes a γ-Al2O3 nanocrystallized mesoporous film for which pores anisotropy value was as high as 4. In this case, the G factor of the Kelvin equation became 1.13; thus, the present pore size determination approach corrected the measured pore size value by nearly 44%.31 (31) Kuemmel, M.; Grosso, D.; Boissiere, C.; Smarsly, B.; Brezesinski, T.; Albouy, P. A.; Amenitsch, H.; Sanchez, C. Angew. Chem. 2005, 44, 4589.
Properties of Mesoporous Thin Films
Figure 7. Evolutions of optical index n and film thickness d of the CS-500 film as a function of RH of two water subsequent adsorption-desorption cycles.
EEP Analysis of the CS-500 Film. The ellipsometric measurements of the refractive index n and thickness d of a CS-500 film were carried out at different RHs of water (reported in Figure 7). Two adsorption-desorption cycles were performed on each film in order to investigate the stability of the films and the rehydration of the silica surfaces. The first isotherm exhibited a low value of refractive index at low RH (n700 nm ) 1.19), which is characteristic, for silica, of the presence of a large fraction of micro and/ or mesopores within a silica film.5,9 With the increasing of RH, very little adsorption was observed up to a RH of 45%. At higher RH, a steep increase of refractive index was observed, characteristic of mesopores filling of water by capillary condensation. After the first adsorptiondesorption cycle, the refractive index at low RH was higher than the original one. This was partly due to a densification of the film induced by the capillary stress produced during the water condensation into mesopores and partly due to the chemisorption of additional matter within the porous network (as checked by FTIR measurements in dry air, not shown here).10,26,32 With the first isotherm, the CS500 film contracted irreversibly from 170.3 to 166.5 nm. (32) Inagaki, S.; Fukushima, Y. Microporous Mesoporous Mater. 1998, 21, 667.
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Figure 8. Evolutions of optical index n and film thickness d of the FS-500 film as a function of RH of two subsequent water adsorption-desorption cycles.
A second adsorption-desorption cycle produced a reversible isotherm with a refractive index n700 value of 1.25 at low humidity. A negligible irreversible contraction of the film was observed ( p >3). In these materials, the use of a spherical (or cylindrical) pores model induces errors higher than 40% on pore size determinations.31 The exact value of p being the crucial point of the pore size determination, multiangle SAXS experiments are carried out at the moment in order to reconstruct accurately the shape and connectivities of porous networks of these films. These data will be used to confirm and further improve the actual contraction model. Appendix I. Development of Kelvin Equation Modified for Ellipsoidal Pore Shapes Kelvin Equation for Ellipsoidal Spheres.
P dS RT ln ) γVL cos θ P0 dV
Hereafter, we calculated the dS/dV factor for a pore with spheric-ellipsoidal shape of anisotropy p equal to the ratio of the ellipse large radius a on small radius b. The resulting ellipsoidal sphere volume and surface expressions are given as function of b and p in eqs 3′ and 3′′, respectively
4 V ) πp2b3 3
(38) Galarneau, A.; Desplantier-Giscard, D.; Di Renzo, F.; Fajula, F. Catal. Today 2001, 68, 191. (39) Galarneau, A.; Cambon, H.; Di Renzo, F.; Fajula, F. Langmuir 2001, 17, 8328. (40) Galarneau, A.; Cambon, H.; Di Renzo, F.; Ryoo, R.; Choi, M.; Fajula, F. New J. Chem. 2003, 1, 73. (41) Xiao, X.; Hata, N.; Yamada, K.; Kikkawa, T. Rev. Sci. Instrum. 2003, 74 (10), 4539.
(3′)
[11 -+ EE]
S ) 2p2b2π + (πb2/E) ln
(3′′)
with
E)
(p2 - 1)1/2 p
the eccentricity factor. Reintroduced into eq 3, we obtain the Kevin equation for ellipsoidal interfaces:
[
]
C P RT ln ) -γVL cos θ 1 + 2 /b P0 2p
Conclusion We validated here for the first time that the EEP technique is able to perform simple, cheap, and accurate determination of PSD, porous volume, pore size, pore accessibility, and orthogonal Young’s modulus of mesoporous thin films. The uniaxial contractions of two types of mesoporous thin films featuring contracted Pm3n and Im3m cubic mesophases were investigated by combination 2D-SAXS and/or EEP. We evidenced a homothetic relation between the film macroscopic contraction and the mesoscopic porous lattice contraction. We proved that the calculation of mesostructure contraction can be done easily by ellipsometry with no need of additional 2D-SAXS experiments. These contraction data were used to calculate the anisotropy of the mesopores via the IIC model. Coupled with a modified Kelvin equation, the IIC model allowed a precise pore size measurement, correcting classical models errors of about 25% in the presented examples.
(3)
(4)
with
ln C)
[11 -+ EE] E
Kelvin Equation for Ellipsoidal Cylinders. In the same way, the Kelvin equation can be modified to describe ordered mesopores with 2D hexagonal pore packing, contracted normally to the c axis of the hexagon. One obtains then the following equation in which b represents the small radius of the ellipsoidal section of a flatten cylinder:
RT ln
1 1 P ) -γVL cos θ 1 + /b P0 2 p
[(
)]
Supporting Information Available: Schematic representation of the FS-500 porous network resulting of the contraction of an Im3m mesostructure along the [110] direction. This material is available free of charge via the Internet at http://pubs.acs.org. LA050981Z
